MathDB

The management of a secret society is made up of

4

people. To admit new partners they use the following criteria:

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Only the

4

members of the directory vote, being able to do it in

3

ways: in favor, against or abstaining.

\bullet

Each aspiring partner must obtain at least

2

votes in favor and none against. At the last management meeting,

8

requests for admission were examined. Of the total votes cast, there were

23

votes in favor,

2

votes against and

7

abstaining. What is the highest and what is the lowest value that the number of approved admission requests can have on that occasion?

Problem Statement